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Derivation of Lévy-type anomalous superdiffusion from generalized statistical mechanics. (English) Zbl 0829.60073

Shlesinger, Michael F. (ed.) et al., Lévy flights and related topics in physics. Proceedings of the international workshop, held at Nice, France, 27-30 June, 1994. Berlin: Springer-Verlag. Lect. Notes Phys. 450, 269-289 (1995).
Summary: The robustness and ubiquity of the macroscopic normal diffusion is well- known to be derivable within Boltzmann-Gibbs statistical mechanics. It is essentially founded on (i) a variational principle applied to \(S = - \int dxp (x)\ln [p(x)]\) with simple a priori constraints, and (ii) the central limit theorem. Its basic characterization consists in the time evolution \(\langle x^2 \rangle \propto t\). A recently generalized statistical mechanics enables the extension of the same program in order to also cover the long-tail Lévy-like anomalous superdiffusion, a phenomenon frequently encountered in Nature. By so doing, this formalism succeeds where standard statistical mechanics and thermodynamics are known to fail.
For the entire collection see [Zbl 0823.00016].

MSC:

60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
82B30 Statistical thermodynamics
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